Wheatstone bridge

Return to the Index.

This model can be used to determine the null conditions of a Wheatstone bridge or to determine the out-of-null output voltage as a function of arm resistance. Resistors R1 ... R4 are the four arms of the bridge and RL represents the input resistance of the detector or null voltage read-out device. This model requires an iterative solution; the "guess" variable can be the voltage or current in any one of the arms. In the example variable sheet shown below, an off-null sensitivity of 24.8 mV per ohm is demonstrated for a nearly balanced 100 ohm bridge with an excitation voltage of 10 volts and RL=100K. 

Variable Sheet
_________________________________________________________________________________
St Input     Name    Output    Unit      Comment
             E1      4.9751369 volts     Voltage across R1 (volts, mV, µV)
             I1      .04975137 Amps      Current through R1 (Amps, mA, µA)
   100       R1                Ohms      Resistance of arm 1 (Ohms, Kohms, MOhms)
             E2      4.9999876 volts     Voltage across R2 (volts, mV, µV)
             I2      .04999988 Amps      Current through R2 (Amps, mA, µA)
   100       R2                Ohms      Resistance of arm 2 (Ohms, Kohms, MOhms)
             E3      5.0248631 volts     Voltage across R3 (volts, mV, µV)
             I3      .04975112 Amps      Current through R3 (Amps, mA, µA)
   101       R3                Ohms      Resistance of arm 3 (Ohms, Kohms, MOhms)
             E4      5.0000124 volts     Voltage across R4 (volts, mV, µV)
             I4      .05000012 Amps      Current through R4 (Amps, mA, µA)
   100       R4                Ohms      Resistance of arm 4 (Ohms, Kohms, MOhms)
             EL      24.85071  mV        Voltage across RL (volts, mV, µV)
             IL      2.4851E-7 Amps      Current through RL (Amps, mA, µA)
   100000    RL                Ohms      Resistance of detector (Ohms, Kohms, MOh
   10        Vb                volts     Excitation voltage (volts, mV, µV)


Rule Sheet
_________________________________________________________________________________
S Rule
* E1=I1*R1  "Ohms Law for R1
* E2=I2*R2  "Ohms Law for R2
* E3=I3*R3  "Ohms Law for R3
* E4=I4*R4  "Ohms Law for R4
* EL=IL*RL  "Ohms Law for RL
* E1+E3=Vb  "Kirchoffs Law for voltage
* E2+E4=Vb  "Kirchoffs Law for voltage
* I1=I3+IL  "Kirchoffs Law for current
* I2=I4-IL  "Kirchoffs Law for current
* EL=E3-E4  "Kirchoffs Law for voltage